So let's say that I received an answer that like and accepted it. While I have read How do I close my own question?, I do not nearly have enough reputation points to do that. If such a feature doesn't exist can it be created? People like me should be able to do that if they want to.
Only questions that aren't a good fit for the site should be closed, it isn't the equivalent of saying "this question is solved" but rather "this question doesn't meet the quality standards of this site". Closed questions are always closed with a specific reason, such as "Unclear what you're asking", "Too broad" or "Primarily opinion-based".
Accepting an answer is the only way you have to show that your issue is solved.
Stack Exchange Q&A's are however not only for you but future readers so there is no reason to prevent further answers.
Yes, there is. You can only close your question if it is a duplicate of another question. If not, you need the appropriate reputation to vote to close on any question.
The most interesting question is: why do you want to close it? You say because you don't want other answers any more. Isn't that just a little selfish? Someone is trying to help you and you just want them to go away? For what?
As long as your question is on-topic it should stay on the site. Think of the hundreds of other people coming at your question. They can be helped by a new and better answer. Why deny them that?
I think this all started with the idea that SE is your personal assistant where you can get your answer for no effort. It is not! We try to make the site a useful knowledge repository for everyone, including you.